tess.nTaxa.expected {TESS}

tess.nTaxa.expected: The expected number of taxa at present of a tree under a global, time-dependent birth-death process ( E[ N(T) ] )

Description

tess.nTaxa.expected computes the expected number of taxa at the present time T (the process start at time s and times increases until the present) under time-dependent. The rates may be any positive function of time or a constant. Additionally, mass-extinction event can be provided and a uniform taxon sampling probability. You have several options for the start of the process (origin vs MRCA). One important feature is that you can compute the expected number of taxa under the reconstructed process, that is, only lineages that survive until the present.

Usage

tess.nTaxa.expected( begin,
			   t,
			   end,
			   lambda,
			   mu,
			   massExtinctionTimes=c(),
			   massExtinctionSurvivalProbabilities=c(),
			   samplingProbability=1.0,
			   MRCA=TRUE,
			   reconstructed=FALSE)

Arguments

begin

The time when the process starts.

t

The time at which we want to know the expected number of lineages (could be equal to end).

end

The time when the process end (e.g. the present).

lambda

The speciation rate function or constant.

mu

The extinction rate function or constant.

massExtinctionTimes

The set of mass-extinction times after the start of the process.

massExtinctionSurvivalProbabilities

The set of survival probabilities for each speciation event. The set must have the same length as the set of mass-extinction times.

samplingProbability

The probability for a species to be included in the sample.

MRCA

Does the process start with the most recent common ancestor? If not, the tree must have a root edge!

reconstructed

Are we computing the expected number of lineage at time t in the reconstructed process?

Value

Returns the expected number of taxa.

Author(s)

Sebastian Hoehna

References

S. Hoehna: Fast simulation of reconstructed phylogenies under global, time-dependent birth-death processes. 2013, Bioinformatics, 29:1367-1374

Examples

# create the time-dependent speciation and extinction rate functions
# here we use episodic functions
l <- Vectorize(function(x) { if (x > 0.5 || x < 0.3) { return (1) } else { return (2) } })
e <- Vectorize(function(x) { if (x > 0.5 || x < 0.3) { return (0.95) } else { return (0.5) } })

# now we can compute the expected number of taxa at time t
# note that we compute here the actual diversity at time t
# if you set reconstructed=TRUE, then you get the expected
# number of lineages that will survive until the present
tess.nTaxa.expected(begin=0,t=2,end=5,l,e,MRCA=TRUE)